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A nucleus with mass number 240 breaks into ....

A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding energy per nucleon of unfragmented nucleus is 7.6 MeV while that of fragments is 8.5 MeV. The total gain in the binding energy in the process is:

(1) 0.9 MeV
(2) 9.4 MeV
(3) 804 MeV
(4) 216 MeV

Solution

B.E. of unfragmented nucleus = $7.6 \times 240 $ MeV = $15.2 \times 120 $ MeV

B.E. of fragments = $8.5 \times 120 + 8.5 \times 120 $ MeV = $17 \times 120 $ MeV

Gain in B.E. = $17\times 120 - 15.2 \times 120 $ MeV = $1.8 \times 120 $ MeV = 216 MeV

Answer: Option (4)